Unlabeled Trees: Distribution of the Maximum Degree

Pick a tree uniformly at random from among all unlabeled trees on n vertices, and let Xn be the maximum of the degrees of its vertices. For any fixed integer d, as n∞, where μn = c1 log n, where {μn} : = μn – ⌊μ⌋ denotes the fractional part of μn and where co, c1, and η∞ are knnown constants, givenb approximately by c0 = 3.262 …, c1 = 0.9227 …, and η∞ = 0.3383…. © 1994 John Wiley & Sons, Inc.